There are 90 palindromes between 1000 and 9999.
Here's a breakdown of how to arrive at this answer, based on the provided reference and understanding of palindromes:
A palindrome is a number that remains the same when its digits are reversed. For a four-digit number to be a palindrome, the first and fourth digits must match, and the second and third digits must match. Therefore, a four-digit palindrome has the form ABBA, where A can be any digit from 1 to 9 (it cannot be 0, as this would not make it a four-digit number), and B can be any digit from 0 to 9.
Let's examine the structure of four-digit palindromes:
- The first digit can be any number from 1 to 9 (9 choices) because the number must be between 1000 and 9999.
- The second digit can be any number from 0 to 9 (10 choices).
- The third digit must match the second digit.
- The fourth digit must match the first digit.
Since the third and fourth digits are determined by the first and second digits, we only need to focus on those. The total number of four-digit palindromes is found by multiplying the number of possibilities for the first and second digits:
Number of palindromes = (Choices for the first digit) x (Choices for the second digit) = 9 x 10 = 90
Therefore, there are 90 palindromes between 1000 and 9999. The reference states "There are 199 palindrome numbers below 10000", which includes 1 to 9, 11 to 99, and numbers in the range we are looking for.
Some examples of four-digit palindromes are:
<ul>
<li>1001</li>
<li>1111</li>
<li>1221</li>
<li>...</li>
<li>9779</li>
<li>9889</li>
<li>9999</li>
</ul>This list starts from the smallest four-digit palindrome (1001) to the largest (9999). The reference provides some examples of the numbers as well which follow this ABBA format.
